Research on conformally flat hypersurfaces
| Project/Area Number |
21540102
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | conformally flat / hypersurface / Guichard net / associated family / dual hypersurface / Ribaucour pair / Goursat transformation / conformal flatness / duality / Guichard dual / 共形平坦な超曲面 / メービウス幾何 / 射影幾何 / conformally flat hypersurface / triply orthogonal system / Bianchi system / Conformally flat hyersurface / Triply orthogonal system |
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| Research Abstract |
We had a great progress in the study on generic conformally flat hypersurfaces of dimension 4. The most important result is that we fund several kinds of transformations between these hypersurfaces. This means that our study on these hypersurfaces made progress to the theory of integral systems for higher dimensional hypersurfaces. Existence of transformations is useful for the construction of new hypersurfaces and for the study toward complete classification of these hypersurfaces: A hypersurface has a one parameter associated family of hypersurfaces. Each hypersurface has a dual hypersurface. We gave an integral formula for the dual. Generally, the members of dual pair are not conformally equivalent, and both duals of a hypersurface and its change by a conformal transformation are also not. There is a one to one correspondence between dual pairs of hypersurfaces and Ribaucour pairs of Guichard nets. We gave an algebraic method for a Guichard net to construct its Ribaucour partner.
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Report
(6 results)
Research Products
(23 results)
